Collective excitations of Λ hypernuclei

Transcription

1 Collective excitations of Λ hypernuclei Kouichi Hagino (Tohoku Univ.) J.M. Yao (Southwest Univ.) Z.P. Li (Southwest Univ.) F. Minato (JAEA) 1. Introduction 2. Deformation of Lambda hypernuclei 3. Collective rotational excitations of hypernuclei 4. Vibrational excitations of spherical hypernuclei 5. Summary Λ

2 Introduction Impurity effects: one of the main interests of hypernuclear physics how does Λ affect several properties of atomic nuclei? Ø size, shape, density distribution, single-particle energy, shell structure, fission barrier the most prominent example: the reduction of B(E2) in 7 Λ Li α d 6 Li 9.3 +/- 2.1 e 2 fm / /- 0.5 e 2 fm 4 α+λ 7 Λ Li about 19% reduction of nuclear size (shrinkage effect) K. Tanida et al., PRL86( 01)1982 d

3 How about heavier nuclei? sd-shell nuclei Ikeda diagram A excitation energy clusterization ground state series (shell model structure) ground state : a shell model-like structure (for nuclei heavier than Be) cluster-like structure: appears in the excited states (the threshold rule)

4 Shell model (mean-field) structure and nuclear deformation Ø many open-shell nuclei are deformed in the ground state ü characterstic feature of finite many-body systems ü spontaneous symmetry breaking of (rotational) symmetry Ø B(E2) for deformed nuclei A change in B(E2) can be interpreted as a change in β

5 sd-shell nuclei:prominent nuclear deformation an evidence for deformation rotational spectrum (MeV) Mg How is the deformation altered due to an addition of Λ particle?

6 Self-consistent mean-field (Hartree-Fock) method: independent nucleons in a mean-field potential optimized shape can be automatically determined = suitable for a discussion on shape of hypernuclei Ø First application to deformed hypernucleus J. Zofka, Czech. J. Phys. B30( 80)95 Hartree-Fock calculations with V NN : 3 range Gauss V ΛN : 2 range Gauss Λ changes the Q-moment (deformation) at most by 5% e.g., β = 0.5 β=0.475

7 Shape of hypernuclei RMF for deformed hypernuclei quark model 17 Λ O variational principle cf. D. Vretenar et al., PRC57( 98)R1060 Λσ and Λω couplings etc. self-consistent solution (iteration)

8 RMF for deformed hypernuclei self-consistent solution (iteration) (intrinsic) Quadrupole moment Application to hypernuclei Ø parameter sets: NL3 and NLSH Ø Axial symmetry Ø pairing among nucleons: Const. gap approach (MeV) Ø Λ particle: the lowest s.p. level (K π =1/2 + ) Ø Basis expansion with deformed H.O. wf Ø Deformation parameter: (fm)

9 Ne isotopes Si isotopes l in most cases, similar deformation between the core and the hypernuclei l hypernuclei: slightly smaller deformation than the core Exception: 29 Λ Si oblate ( 28 Λ Si) spherical ( 29 Λ Si) Myaing Thi Win and K.H., PRC78( 08)054311

10 Potential energy surface (constraint Hartree-Fock) a flat energy curve a large change in nuclear deformation due to a Λ particle the same conclusion also with NLSH and/or with constant G approach to pairing Myaing Thi Win and K.H., PRC78( 08)054311

11 Another example: 13 Λ C cf. recent AMD calculations oblate spherical Myaing Thi Win and K.H., PRC78( 08) M. Isaka, K. Kimura, A. Dote, and A. Ohnishi, PRC83( 11)044323

12 3D Hartree-Fock calculation for hypernuclei So far, axial symmetric shape has been assumed for simplicity Effect of Λ particle on triaxial deformation? θ,φ z Courtesy: Takeshi Koike

13 Skyrme-Hartree-Fock calculations for hypernuclei 3D calcaulations with non-relativistic Skyrme-Hartree-Fock: the most convenient and the easiest way Ø zero-range interaction Ø 3D mesh calculation ( lattice Hartree-Fock ) Ø Imaginary time evolution of single-particle wave functions Ø computer code ev8 available P. Bonche, H. Flocard, and P.-H. Heenen, NPA467( 87)115, CPC171( 05)49 extension to hypernuclei M. Rayet, NPA367( 81)381 c.f. axially symmetric SHF calculations: X.-R. Zhou et al., PRC76( 07)

14 24 Mg, 25 ΛMg (Interaction No.1 of Yamamoto et al. + SGII (NN)) +Λ Ø Deformation is driven to speherical when Λ is in the lowest state Ø Prolate configuration is prefered for the same value of β Myaing Thi Win, K.H., T. Koike, Phys. Rev. C83( 11)014301

15 c.f. 3D RMF calculations B.-N. Lu, E.-G. Zhao, S.-G. Zhou, PRC84( 11)014328

16 Rotational Excitation of Λ hypernuclei Collective spectrum of a single-λ hypernucleus: a half-integer spin Bohr Hamiltonian for the core part: mass inertias: cranking approximation (Inglis-Belyaev formula for the rotational inertia)

17 Solution of Collective H fluctuation of deformation parameters J.M. Yao, Z.P. Li, K.H. et al., NPA ( 11)12 much smaller change

18 reduction of B(E2) from 2 + to Mg: B(E2) = 62.0 e 2 fm 4 J.M. Yao, Z.P. Li, K.H. et al., NPA ( 11)12 25 Λ Mg: B(E2) = 56.4 e 2 fm 4 (about 9% reduction) cf. AMD calculation for 25 ΛMg (M. Isaka et al., PRC85( 12)034303)

19 Vibrational Excitation of spherical Λ hypernuclei RPA: linear superposition of many 1p1h sates ü low-lying collective motions ü Giant Resonances of ordinary nuclei K. Yoshida and T. Nakatsukasa, PRC83( 11)021304(R)

20 Application to 18 ΛΛ O Skyrme HF + RPA SkM* + Yamamoto No. 5 + Lanskoy SΛΛ1 low-lying collective states nucleus E (MeV) B(E2) (e 2 fm 4 ) E(MeV) B(E3) (e 2 fm 6 ) 16 O ΛΛ O F. Minato and K.H., PRC85( 12)924316

21 shifts toward high energy moderate shifts large shift low-lying collective states nucleus E (MeV) B(E2) (e 2 fm 4 ) E(MeV) B(E3) (e 2 fm 6 ) 16 O ΛΛ O

22 Dipole motion dipole motion of Λ particles around the core nucleus New dipole mode! cf. soft dipole motion in neutron-rich nucleus K. Ikeda, T. Myo, K. Kato, and H. Toki, Lecture Note in Phys., vol. 818

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24 Summary Shape of Λ hypernuclei: from the view point of mean-field theory Ø deformation: an important key word in the sd-shell region Ø RMF: stronger influence of Λ particle Shape of 28 Si : drastically changed due to Λ Ø SHF: weaker influence of Λ, but large def. change if PES is very flat 3D calcaulations softening of γ-vibration? Rotational excitations of Λ hypernuclei Ø about 9% reduction of B(E2) value for 24 Mg Vibrational excitations of Λ hypernuclei Ø New dipole mode A challenging problem Ø full spectrum of a single Λ hypernucleus odd mass, broken time reversal symmetry, half-integer spins